Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Rational Invariants of certain Orthogonal and Unitary Groups

Rational Invariants of certain Orthogonal and Unitary Groups RATIONAL INVARIANTS OF CERTAIN ORTHOGONAL AND UNITARY GROUPS D. CARLISLE AND P. H. KROPHOLLER The purpose of this note is to prove a conjecture of Huah Chu [1] on modular rational invariants of finite orthogonal groups. In an appendix we briefly describe how similar results can be proved for unitary groups. Recently, in [2], S. D. Cohen established a special case of Huah Chu's conjecture, and here we adopt Cohen's notation. Thus q is an odd prime power, n is a positive integer, V = F£ is an n- dimensional vector space over ¥ = GF{q) and Q (x ...,x ) is a non-degenerate g n lt n quadratic form on V. Without loss of generality we may assume that X X = X Qn( l> • • •' n) iLjA-K k> where the A eF are non-zero. Here we write fc ff P -IV J Y A A ''O ~~ 2 La fc *> and for i; ^ 1, In the notation of [2] we have Q (i) = £,/2 for i ^ 1 and Q (0) = £ . As in [2], we write n n 0 K for the field F (x ... , x ) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Rational Invariants of certain Orthogonal and Unitary Groups

Download PDF
4 pages

Loading next page...
 
/lp/wiley/rational-invariants-of-certain-orthogonal-and-unitary-groups-fy6Y8idMvF

References (0)

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/24.1.57
Publisher site
See Article on Publisher Site

Abstract

RATIONAL INVARIANTS OF CERTAIN ORTHOGONAL AND UNITARY GROUPS D. CARLISLE AND P. H. KROPHOLLER The purpose of this note is to prove a conjecture of Huah Chu [1] on modular rational invariants of finite orthogonal groups. In an appendix we briefly describe how similar results can be proved for unitary groups. Recently, in [2], S. D. Cohen established a special case of Huah Chu's conjecture, and here we adopt Cohen's notation. Thus q is an odd prime power, n is a positive integer, V = F£ is an n- dimensional vector space over ¥ = GF{q) and Q (x ...,x ) is a non-degenerate g n lt n quadratic form on V. Without loss of generality we may assume that X X = X Qn( l> • • •' n) iLjA-K k> where the A eF are non-zero. Here we write fc ff P -IV J Y A A ''O ~~ 2 La fc *> and for i; ^ 1, In the notation of [2] we have Q (i) = £,/2 for i ^ 1 and Q (0) = £ . As in [2], we write n n 0 K for the field F (x ... , x )

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Jan 1, 1992

There are no references for this article.